Energy-distance-based two-sample testing in the presence of incomplete data

Abstract

The problem of two-sample testing is addressed in the presence of missing data under general missingness mechanisms. The focus is placed on the widely used energy-based two-sample test. In addition to the standard complete case analysis, we introduce a novel adaptation of the test statistic that incorporates all available data, as well as two resampling procedures for p-value approximation. Furthermore, we present a new bootstrap procedure tailored for scenarios where the test statistic is computed on imputed data using standard imputation techniques. Through a comprehensive simulation study, the proposed methods are evaluated across a range of sample sizes, dimensions, data distributions, missingness mechanisms, and missing data proportions. Practical guidelines are offered based on the observed performance in each scenario.